Answer:
x = 18.0
Step-by-step explanation:
We know that a tangent and a radius create a right angle at the point of tangency, or where they meet at a point on the given circle (tangent radius theorem).
Now we can say that triangle TSP is a right triangle.
We can now use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]
We are looking for x, which is the hypotenuse.
[tex]15^{2} +10^{2} =c^{2}[/tex]
First, we'll simplify the exponents
[tex]225 +100 =c^{2}[/tex]
[tex]325=c^{2}[/tex]
C represents the hypotenuse, which means that we need to square root our equation (on both sides, of course) to find the hypotenuse.
[tex]\sqrt{325} =c[/tex]
[tex]\sqrt{325}[/tex] ≈ 18.0
